Question

Consider the following binomial tree. The numbers in squares are stock prices. The numbers in circles will be option prices (# numbers are the exercise numbers to answer your calculation). Today, the stock is at 100 and can go up and down over the next week, and then again up and down from there. We are pricing a call struck at 90. Use the computed q to sweep back through the tree to fill the call values in circles. For each node use the formula: C = q Cu + (1-q) Cd. Ignore interest.

#8 120 110 #11 100 / #9 #13 100 #12 80 #10

Q7: Compute the probability of the up-step: q =

Q8: #8 Call Value =

Q9: #9 Call Value =

Q10: #10 Call Value =

Q11: #11 Call Value =

Q12: #12 Call Value =

Q13: #13 Today’s Call Value=

Q14: Exercise #14. Today, the delta (hedge ratio) is Cu-C A = Su-S

Q15: Exercise #15. Today’s call premium is: $______

Q16:Exercise #16. Interpret the delta. If you sell a call option on one hundred shares, the delta hedge will require you to buy _______________ shares of stock (how many?).

Answer 1

7. Calculate the probability of up-step as follows:

Therefore, the probability of up-step q is 0.5

8. Calculate the #8 call value as follows:

Therefore, the call value at #8 is 30.

9. Calculate the #9 call value as follows:

Therefore, the call value at #9 is 10.

10. Calculate the #10 call value as follows:

Since the price is less than the strike price, the value will be 0.

11. Calculate the #11 call value as follows:

Therefore, the value of call at #11 is 20.

12. Calculate the #12 call value as follows:

Therefore, the value of call at #12 is 5.

13. Calculate the #13 today’s call value as follows:

Therefore, the value of call at #13 is 12.5.

14. Calculate the today’s delta or hedge ratio as follows:

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Therefore, the hedge ratio is 0.75